The proportional hazards regression model is extensively used to analyze the effect of covariates such as age, sex, and treatment on patient survival. The major goals of my research project are: to develop methods of testing whether this model is appropriate for a given data set; to develop techniques for selecting important covariates; to analyze models with random covariate effect; to show how to correct for missing data; to develop methods for measuring strength of prediction and to develop tests appropriate for small data sets. Many clinical studies have multiple endpoints. When patients enter the study their symptoms remit or progress and they eventually die. This research project will show how such data can be analyzed using loglinear models for competing risks and semi-markoff processes. Many clinical and experimental studies on cancer drugs and experiments on chemical carcinogenesis are concerned with estimating how response increases with dose. I propose to develop methods which will make the use of isotonic regression accessible to cancer researchers. I plan to develop isotonic confidence intervals for response at each dose and for the minimum dose at which a response occurs. Such intervals will allow quantification of the uncertainty about the effect of a drug or a carcinogen.